Question 72373
Let the diameter of grapefruits of Texas be {{{D[T]}}} and that of Florida be {{{D[F]}}}.
Let the volume of grapefruits of Texas be {{{V[T]}}} and that of Florida be {{{V[F]}}}.
Therefore, {{{V[T] = k*D[T]^3}}} and {{{V[F] = k*D[F]^3}}} where k = constant of proportionality.
So, {{{V[F]/V[T] = (k*D[F]^3)/(k*D[T]^3)}}}
or {{{V[F]/V[T] = D[F]^3/D[T]^3}}}

Given, {{{D[T] = 2D[F]}}}.
So {{{V[F]/V[T] = D[F]^3/(2D[F])^3 = 1/8}}}


Let the cost of each grapefruit of Texas be {{{C[T]}}} and that of Florida be {{{C[F]}}}.

Given that {{{C[T] = 7C[F]}}}

Then cost per unit volume of grapefruit from Texas is {{{C[T]/V[T]}}} and that of grapefruit from Florida is {{{C[F]/V[F]}}}.


Now, {{{(C[T]/V[T])/(C[F]/V[F]) = (C[T]/C[F])(V[F]/V[T]) = (7)(1/8) = 7/8 < 1}}}


Hence, it is wiser to buy the grapefruits from Texas.